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United States Patent |
5,594,354
|
Roberts
,   et al.
|
January 14, 1997
|
Method for measuring selected frequencies of a coupled-dual resonator
crystal
Abstract
The present invention discloses a method for obtaining frequency parameters
to determine the resonator frequencies, the synchronous peak separation
frequency, and the normal center frequency of a coupled-dual resonator
crystal. Under this method, a plurality of frequencies are applied to a
first electrode. This application is performed once while the second
electrode and the common electrode are connected by a short circuit, and
then again when the second electrode and the common electrode are
capacitively connected or open circuited. During each application of the
plurality of frequencies to the crystal, the phase response for the output
of the resonator circuit is monitored. Then the time response of the
crystal is determined. Next, the time delay relative maxima for the time
response is determined. Finally, the frequencies at which the time delay
relative maxima occur are determined. These frequencies correspond to the
inflection points where the change in phase goes from monotonically
increasing to monotonically decreasing. These frequencies are used to
calculate the resonator frequencies, the synchronous peak separation
frequency, and the normal center frequency of the crystal. Alternatively,
all of the critical frequencies can be determined with the second
electrode and the common electrode connected by a short circuit. In this
case, however, the critical frequencies correspond to the time delay
maxima and minima for the time response. This method is applicable
regardless of the frequencies of the resonators or the amount of frequency
separation between the resonators.
Inventors:
|
Roberts; Gerald E. (Lynchurg, VA);
Roberts; Michael E. (Lynchurg, VA)
|
Assignee:
|
Xtal Technologies, Ltd. (Carle Place, NY)
|
Appl. No.:
|
370495 |
Filed:
|
January 9, 1995 |
Current U.S. Class: |
324/727; 324/76.49; 324/652 |
Intern'l Class: |
G01R 029/22; 76.49; 76.52; 76.77 |
Field of Search: |
324/649,652,653,681,682,683,707,708,709,719,727,76.19,76.21,76.22,76.25,76.39
|
References Cited
U.S. Patent Documents
3963982 | Jun., 1976 | Roberts | 324/727.
|
3992760 | Nov., 1976 | Roberts | 29/25.
|
4093914 | Jun., 1978 | Peppiatt et al. | 324/727.
|
4433316 | Feb., 1984 | Roberts et al. | 333/189.
|
4477952 | Oct., 1984 | Crescenzi et al. | 29/25.
|
4484158 | Nov., 1984 | Roberts et al. | 333/191.
|
4578634 | Mar., 1986 | Healey et al. | 324/727.
|
4627379 | Dec., 1986 | Roberts et al. | 118/721.
|
4676993 | Jun., 1987 | Roberts et al. | 427/10.
|
4833430 | May., 1989 | Roberts et al. | 333/191.
|
4839618 | Jun., 1989 | Roberts et al. | 333/191.
|
5047726 | Sep., 1991 | Roberts et al. | 324/727.
|
5049828 | Sep., 1991 | Toliver et al. | 324/727.
|
5146174 | Sep., 1992 | Toliver et al. | 324/727.
|
5272597 | Dec., 1993 | Staples et al. | 361/816.
|
Other References
Roberts, David A. et al., "On the Four-Frequency Measurement PRocess for
Coupled Dual Resonator Crystals", IEEE Transactions on Instrumentation and
Measurement, vol. 42, No. 5, Oct. 1993, pp. 924-926.
|
Primary Examiner: Wieder; Kenneth A.
Assistant Examiner: Brown; Glenn W.
Attorney, Agent or Firm: Dorsey & Whitney LLP
Claims
What is claimed is:
1. A method of accurately measuring frequencies of a coupled-dual resonator
crystal having a piezoelectric plate, a first electrode on the plate, a
common electrode on the plate, a second electrode on the plate, the method
comprising the steps of:
connecting a frequency synthesizer to the first electrode and to a
reference point;
applying a plurality of frequencies to the first electrode;
monitoring a phase response of the crystal with respect to frequency;
monitoring a time response of the crystal with respect to frequency;
determining time delay relative maxima from the time response; and
determining critical frequencies corresponding to the time delay relative
maxima, whereby the critical frequencies are used in the calculation of
crystal frequency characteristic values, and all of the critical
frequencies and the crystal frequency characteristic values can be
determined and calculated, respectively, at any stage in a fabrication
process without the necessity of re-tuning or re-calibration.
2. The method of claim 1 wherein the common electrode is connected to the
second electrode by a switch, the switch being in a closed position and
the method further comprising the steps of:
determining time delay relative minima of the time response; and
wherein the critical frequencies correspond to the time delay relative
maxima and the time delay relative minima.
3. The method of claim 1, wherein the second electrode is connected to the
common electrode by a capacitor.
4. The method of claim 1, wherein the second electrode and common electrode
are open circuited.
5. A method of accurately measuring frequencies of a coupled-dual resonator
crystal having a piezoelectric plate, a first electrode on the plate, a
common electrode on the plate, and a second electrode on the plate,
wherein a connection of the first electrode and the common electrode forms
a first resonator and a connection of the second electrode and the common
electrode forms a second resonator, the method comprising the steps of:
connecting a frequency synthesizer to the first electrode, wherein an
oscillator creates a plurality of frequencies;
connecting the second electrode and the common electrode so that the second
resonator is short circuited;
applying a plurality of frequencies to the first electrode with the second
resonator short circuited;
monitoring a phase response of the crystal with respect to frequency with
the second resonator short circuited;
monitoring a time response of the crystal with respect to frequency with
the second resonator short circuited;
determining time delay relative maxima for the time response with the
second resonator short circuited;
determining the first set of critical frequencies corresponding to the time
delay relative maxima;
connecting the second electrode and the common electrode so that the second
resonator is open circuited;
applying a plurality of frequencies to the first electrode with the second
resonator open circuited;
monitoring a phase response of the crystal with respect to frequency with
the second resonator open circuited;
monitoring a time response of the crystal with the second resonator open
circuited;
determining time delay relative maxima for the time response with the
second resonator open circuited;
determining a second set of critical frequencies corresponding to the time
delay relative maxima; and
whereby the critical frequencies are used in the calculation of crystal
frequency characteristic values, and all of the critical frequencies and
the crystal frequency characteristic values can be determined and
calculated, respectively, at any stage in a fabrication process without
the necessity of re-tuning or re-calibration.
6. A method of accurately measuring frequencies of a coupled-dual resonator
crystal having a piezoelectric plate, a first electrode on the plate, a
common electrode on the plate, and a second electrode on the plate, the
method comprising the steps of:
connecting a frequency synthesizer to the first electrode, wherein an
oscillator creates a plurality of frequencies;
connecting the second electrode and the common electrode so that the
connection is a short circuit;
applying a plurality of frequencies to the first electrode;
monitoring a phase response of the crystal with respect to frequency;
monitoring a time response of the crystal with respect to frequency;
determining time delay relative maxima and minima for the time response;
and
determining critical frequencies corresponding to the time delay relative
maxima and minima, whereby the critical frequencies can be used in the
calculation of crystal frequency characteristic values, and the critical
frequencies are determined and the crystal frequency characteristic values
calculated at any stage in a fabrication process without the necessity of
re-tuning or re-calibration.
7. A method of accurately measuring frequencies of a coupled-dual resonator
crystal having a piezoelectric plate, a first electrode on the plate, a
common electrode on the plate, and a second electrode on the plate, the
method comprising the steps of:
connecting a frequency synthesizer to the first electrode and to a
reference point;
applying a plurality of frequencies to the first electrode;
monitoring a phase response of the crystal with respect to frequency;
determining inflection points where the change in phase goes from
monotonically decreasing to monotonically increasing; and
determining critical frequencies corresponding to the inflection points,
whereby the critical frequencies are used in the calculation of crystal
frequency characteristic values and all of the critical frequencies and
the crystal frequency characteristic values can be determined and
calculated, respectively, at any stage in a fabrication process without
the necessity of re-tuning or re-calibration.
8. The method of claim 7 wherein the common electrode is connected to the
second electrode by a switch, the switch being in a closed position and
the method further comprising the steps of:
determining the inflection points where the change in phase goes from
monotonically decreasing to monotonically increasing and also where the
change in phase goes from monotonically increasing to monotonically
decreasing, wherein the critical frequencies correspond to the inflection
points.
9. The method of claim 7, wherein the second electrode is connected to the
common electrode by a capacitor.
10. The method of claim 7, wherein the second electrode and common
electrode are open circuited.
11. A method of accurately measuring frequencies of a coupled-dual
resonator crystal having a piezoelectric plate, a first electrode on the
plate, a common electrode on the plate, and a second electrode on the
plate, the method comprising the steps of:
connecting a frequency synthesizer to the first electrode, wherein an
oscillator creates a plurality of frequencies;
connecting the second electrode and the common electrode so that the
connection is a short circuit;
applying a plurality of frequencies to the first electrode;
monitoring a phase response of the crystal with respect to frequency;
determining inflection points where the change in phase goes from
monotonically decreasing to monotonically increasing and also where the
change in phase goes from monotonically increasing to monotonically
decreasing; and
determining critical frequencies corresponding to the inflection points,
whereby the critical frequencies are used in the calculation of crystal
frequency characteristic values and all of the critical frequencies and
the crystal frequency characteristic values can be determined and
calculated, respectively, at any stage in a fabrication process without
the necessity of re-tuning or re-calibration.
Description
TECHNICAL FIELD
The present invention is generally related to a process for determining
parameters of a monolithic coupled-dual resonator crystal. It is directed
to a process to determine the resonator frequencies, the normalized center
frequency and the synchronous peak separation frequency of crystals at
higher fundamental and overtone frequencies and/or having relatively high
resonator resistances.
BACKGROUND OF THE INVENTION
Such crystals are used extensively in the radio communication industry.
Exemplary uses include IF filter and discriminator applications in mobile
and cellular radios. Coupled-dual resonator crystals are preferred in many
applications because they provide the characteristics of a very narrow
filter due to the extremely high Q of the associated crystal resonators.
Such very narrow filter characteristics are virtually impossible or
extremely difficult to realize with lumped devices, such as inductors and
capacitors.
At the time the original Peppiatt and Roberts methodology was invented, as
taught in U.S. Pat. No. 4,093,914, coupled-dual resonator crystals were
designed to operate at frequencies only as high as the low 20 megahertz
("MHz") range. Currently, units at 45 MHz and 57.5 MHz are routinely built
in production. Because of the requirements for higher and higher IF
frequencies for cellular and mobile radios, with units in the 70 MHz to 90
MHz frequency range being used or considered in new product applications,
the requirement for superior measurement accuracy for such high frequency
coupled-dual resonator crystals is vitally important for testing and
fabricating coupled-dual crystals and for producing high frequency
monolithic crystal filters which meet the new radio specifications.
Key characteristics of these coupled dual crystals must be measured during
the fabrication process as well as at the final test operation. A need
exists for a reliable, accurate, and repeatable process for determining
these characteristics of a coupled-dual resonator crystal. In particular,
four critical frequencies, F1, F2, F3, and F4 must be determined in order
to calculate first and second resonator frequencies, the normalized center
frequency, and the synchronous peak separation frequency. U.S. Pat. No.
4,093,914 discloses a process for measuring the four critical frequencies
in coupled-dual resonator crystals and the formulas for determining the
resonator frequencies, the normalized center frequency, and the
synchronous peak separation frequency. The Peppiatt and Roberts methods
involve determining four critical frequencies by monitoring, in the first
case, one of the two crystal ports while shorting the second port. In the
second case, they are determined by monitoring one of the two crystal
ports while shorting the second port to obtain two frequencies and
effectively open circuiting the second port or connecting a capacitor
across it to obtain the other two frequencies. In the third case, taught
in U.S. Pat. No. 5,047,726, the four critical frequencies are obtained by
first monitoring the first port with the second port effectively open
circuited, or with a capacitor connected across the second port, to obtain
two of the frequencies, and then by monitoring the second port with the
first port short circuited to obtain the other two critical frequencies.
In each of the three cases, each of the four critical frequencies
corresponds to the zero phase crossing of the voltage phase response at or
near the particular voltage amplitude maximum or minimum for the
particular case in question.
It was discovered in U.S. Pat. No. 5,049,828 that as the desired
fundamental or overtone operating frequencies of such coupled-dual
resonator crystals increase and/or the effective resonator resistances
increase, the measured phase excursions below the zero phase reference
diminish and eventually fail to cross the zero phase reference. Also, it
was additionally discovered that where one of the resonator frequencies
(FA, for example) is much lower than that of the other resonator frequency
(FB), the voltage amplitudes associated with two of the measured
frequencies (F1 and F2) will be markedly higher than the voltage amplitude
associated with the other two and the latter may not exhibit excursions
below the zero phase reference.
Since such zero crossings are necessary for accurate frequency
measurements, U.S. Pat. No. 5,049,828 to Toliver et al. discloses a
compensation circuit to establish these zero phase reference points in the
Peppiatt and Roberts transmission measurement system when applied to high
frequency and/or high resonator resistance crystals. However, there are
several problems with the compensation approach disclosed in the Toliver
patent. It adds at least two additional circuit elements to the original
fixture shown in FIG. 4 of U.S. Pat. No. 5,049,828 and it must be set or
tuned to produce the required zero phase crossings. It is usually tuned to
produce the four frequencies at the final crystal test operation. It,
therefore, tends to have accuracy problems at frequencies other than final
frequency. Separate fixtures must be used for coupled-dual resonator
crystals in different frequency ranges. There also tend to be correlation
problems from fixture to fixture whenever a fixture must be set by a
variable coil/capacitor combination.
Therefore, the need arises as to how to determine the values of the four
critical frequencies, F1, F2, F3 and F4, for the cases taught in U.S. Pat.
Nos. 4,093,914, 5,047,726 and 5,049,828 for those situations where the
phase responses do not provide undiminished zero phase crossings without
external compensation.
SUMMARY OF THE INVENTION
To achieve these objects, the present invention discloses a method for
obtaining the necessary frequency measurements to determine the resonator
frequencies, the synchronous peak separation frequency, and the normal
center frequency of the crystal. Under this method, a plurality of
frequencies are applied to the first (or input) electrode of the crystal.
In the preferred method, this approach is performed once while the second
(or output) electrode and the common electrode are connected by a short
circuit, and then again when the second electrode and the common electrode
are open-circuited or connected with a capacitor.
During each application of the plurality of frequencies to the coupled-dual
resonator crystals, the phase response of the driving point impedance is
monitored via a voltage divider network as shown in FIG. 4A. Next, the
time delay relative maxima which occur when the change in phase changes
from monotonically decreasing to monotonically increasing are determined.
Finally, the frequencies at which the time delay relative maxima occur are
the critical frequencies (F1, F2, F3 and F4). These critical frequencies
are used to calculate the resonator A frequency (FA), resonator B
frequency (FB), the synchronous peak separation frequency (SPSF), and the
normal center frequency (NCF) of the crystal.
This preferred process constitutes use of the time delay maxima for
determining the four critical frequencies in case II of the four frequency
measurement process taught in U.S. Pat. Nos. 4,093,914 and 5,047,726. It
encompasses cases I and III taught in those patents as well. This process
is believed to be applicable regardless of the frequencies of the
resonators, the size of the intrinsic coupling between the resonators or
the values of resonator resistances.
Using this method, the calculation of FA, FB, SPSF and NCF can be made very
repeatably and very accurately at any step in the fabrication process. By
not requiring an external compensation circuit, this novel measurement
process provides a more accurate as well as more versatile measurement
process since no re-tuning or re-calibration is required. The invention
provides for improved crystal fabrication techniques, precision evaluation
and testing of high frequency units, and the use of the present invention
ultimately results in lower cost units with improved quality. It is an
object of the present invention to provide a method of determining certain
critical frequencies (i.e., F1, F2, F3, and F4) for coupled-dual resonator
crystals operating at any frequency.
It is an object of the present invention to provide a method of calculating
FA, FB, SPSF and NCF for much higher frequency coupled-dual resonator
crystals.
It is an object of the present invention to determine the critical
frequencies and calculate FA, FB, SPSF and NCF without the use of an
external compensation circuit.
It is an object of the present invention to provide a method of determining
the critical frequencies and calculating FA, FB, SPSF and NCF at any stage
of the fabrication process without the need for re-tuning or
re-calibration.
It is an object of the present invention to provide a method of accurately
and repeatably determining the critical frequencies and calculating FA,
FB, SPSF and NCF that provides results independent of resonator
resistances.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view of a coupled-dual resonator crystal.
FIGS. 2A and 2B show the active and ground sides of mounted crystals.
FIG. 3 illustrates an equivalent circuit of a coupled-dual resonator
crystal.
FIGS. 4A and 4B show the voltage divider network and the fixture
realization for obtaining the four frequencies, F1, F2, F3 and F4.
FIG. 5 shows the connection of a Network Analyzer/S-parameter test set to
the test fixture.
FIGS. 6A through 6H show voltage amplitude, phase, and time responses
explaining the method of the present invention for a 11.2 MHz crystal.
FIGS. 7A through 7J show voltage amplitude, phase, and time responses
explaining the method of the present invention for a 21.4 MHz crystal.
FIGS. 8A through 8J show voltage amplitude, phase, and time responses
explaining the method of the present invention for a 70.2 MHz crystal.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Typically a coupled-dual resonator crystal in its simplest form is
constructed in a manner generally shown in FIGS. 1, 2A and 2B. Such
crystal structure includes a first and second resonator each formed by a
pair of thin film electrodes (14 and 22, 16 and 24, respectively)
deposited on opposite sides of a piezoelectric wafer (12) with electrical
connections to the electrodes being made by way of leads 18, 20, 26 and
28. Although rectangular electrodes are illustrated, circular and
semi-circular electrodes, for example, may also be used. FIG. 3 shows an
equivalent circuit 32 of the coupled-dual resonator crystal 30 shown in
FIGS. 1, 2A and 2B.
Initial nominal electrode dimensions in such structures are conventionally
obtained through the use of precision masking techniques or laser
machining operations as explained in commonly assigned U.S. Pat. No.
4,839,618. Subsequent measuring and manufacturing steps are performed
leading to the last operation prior to sealing, namely, the final
frequency adjustment process. This last operation is extremely critical
since the two resonator frequencies (FA and FB) and the synchronous peak
separation frequency (SPSF), as defined in commonly assigned U.S. Pat. No.
4,093,914, must be precisely controlled in order to obtain a coupled-dual
resonator crystal of desired characteristics. Such criticality is even
further heightened where the desired characteristics include those
required for use in a high quality mobile radio IF filter with operating
frequencies above about 45 MHz, for example, or with one or both effective
resonator resistance values sufficiently large as compared to the
effective resonator reactances. That is to say, such criticality exists
any time that the combination of motional resistance and reactance for a
mode of vibration is such that phase values corresponding to one or both
voltage amplitude maxima associated with the driving-point impedance would
fail to cross zero phase when using the conventional approach of the
4,093,914 patent.
As indicated in the Peppiatt and Roberts '914 patent, the coupled-dual
resonator crystal 30 shown in FIG. 3 is positioned such that its
driving-point impedance, Z, is displayed in a voltage divider network 34
shown in FIG. 4A, from which the four frequencies are obtained for Cases I
and II as taught by Peppiatt and Roberts and Case III as taught by Roberts
et al. in U.S. Pat. No, 5,047,726. The actual test fixture 36 realization
of FIG. 4A is shown in FIG. 4B where switch S1 is used to short-circuit
the B resonator 16 of the crystal 30 or open circuit it (or put a
capacitor C3 across the resonator terminal and the crystal common
terminal).
More specifically, the frequencies F1 through F4 are measured using a
circuit as illustrated in FIG. 4B with a frequency synthesizer connected
at J1 and the A and B probes of a vector voltmeter connected to J2 and J3,
respectively. Frequencies F2 and F4 are obtained when the A side of the
coupled-dual resonator is driven by a frequency synthesizer with the B
side effectively open circuited (or a capacitor C3 is connected across the
B side). Frequencies F1 and F3 are obtained in a similar manner but with
the B side short circuited. Thereafter, key crystal parameters such as
resonator frequencies (FA and FB), normalized center frequency (NCF) as
well as the synchronous peak separation frequency (SPSF) may be calculated
using the F1 through F4 frequencies and the equations taught in the
Peppiatt and Roberts patent.
The appropriate voltage amplitude and phase information is available at the
vector voltmeter B-probe. By monitoring probe J3, the time response, T,
can be generated from the phase information using T=-[d.O
slashed./d.omega.]=-[1/(2.pi.)][d.O slashed./df], where .O slashed. is
voltage phase, .omega. is radian frequency, and f is frequency.
The appropriate relative maxima and relative minima of the resulting time
response can then be used to determine the appropriate four frequencies
for any of the three cases. However, it is preferred to use a Network
Analyzer/S-parameter test set in place of both the frequency synthesizer
and vector voltmeter because the Network Analyzer/S-parameter test set 38
allows for obtaining the time response directly.
FIG. 5 shows the configuration with the analyzer 38 port 1 connected to J1
of the test fixture 36 and port 2 connected to J3 of the fixture 36.
Network Analyzer/test sets such as the HP8751A or HP3577A are of the type
appropriate for determining a time response directly. The preferred
embodiment is the usage of time delay relative maxima (and relative minima
for case I) in case II, but it is equally valid for cases I and III.
The Network Analyzer/S-parameter test set 38 is used as connected in FIG. 5
with the crystal 30 inserted into the fixture 36 as in FIG. 4B. The
S-parameter, S.sub.21, is monitored and is a measure of output voltage
amplitude and phase relative to a reference input voltage and phase. The
reference output voltage, phase and time delay lines are set using a short
in the socket (dotted box in FIG. 4B) from point A to common point G.
Also, the various ranges and scales are set on the analyzer 38. All of
this basically initializes the analyzer 38. The crystal 30 is inserted in
the fixture 36 after the short is removed. Then the internal synthesizer
of the analyzer 38 is swept over the frequency range of interest with S1
closed. Frequencies F1 and F3 are read at the time delay relative maxima.
Then S1 is opened either open circuiting the B-port (or B-side) of the
crystal or connecting a capacitor C3 across the B-side. The internal
synthesizer of the analyzer 38 is again swept over the frequency range of
interest, and frequencies F2 and F4 are read at the time delay relative
maxima. It is noted in FIGS. 6H, 7J and 8J, the frequencies F2 and F4
occur at the frequencies associated with marks 1 and 3. Then equations
(1), (2) and (3), provided below, are used to calculate FA, FB and SPSF.
Since the time delay relative maxima associated with F1 and F3 are in the
mathematical neighborhood of the corresponding amplitude relative maxima,
it is convenient to find the amplitude relative maxima first and then
determine the time delay relative maxima from the time delay response to
obtain F1 and F3, and likewise for F2 and F4.
As indicated in U.S. Pat. Nos. 4,093,914 and 5,047,726, both of which are
herein incorporated in full by reference, it is clear that this process
lends itself to automatic programming with a number of different
algorithms depending on what type of Network Analyzer/S-parameter test set
or frequency synthesizer/vector voltmeter or similar equipment is used. In
essence, the detailed process outlined above is one type of general
algorithm for determining F1, F2, F3 and F4 for case II.
In case II, the F1, F2, F3 and F4 frequencies occur at inflection points
where the change in phase goes from monotonically decreasing to
monotonically increasing (concave down to concave up). In addition, [d.O
slashed./d.omega.] goes from decreasing to increasing, therefore, time
delay becomes T=-[d.O slashed./d.omega.]=-[1/(2.pi.)][d.O slashed./df]
which shows that time delay T goes from increasing to decreasing which is
a relative maxima at those points.
As shown in U.S. Pat. No. 5,047,726, case III follows case II with regard
to using time delay for F1, F2, F3 and F4. In case I, F2 and F4 are
determined by detecting the time delay relative minima when the switch S1
is closed.
Once the critical frequencies are obtained, the resonator A frequency (FA),
the resonator B frequency (FB), the normalized center frequency of the
crystal 30 (NCF), and the synchronous peak separation frequency (SPSF) can
be determined by the equations disclosed in U.S. Pat. No. 4,093,914, as
provided below for case II:
FA=[(F2.sup.2 F4.sup.2 -F1.sup.2 F3.sup.2)/(F2.sup.2 +F4.sup.2 -F1.sup.2
-F3.sup.2)].sup.1/2 (1)
FB=[F2.sup.2 +F3.sup.2 -FA.sup.2 ].sup.1/2 (2)
NCF=[F1F3].sup.1/2 (3)
SPSF=[(FA.sup.2 FB.sup.2 -F1.sup.2 F3.sup.2)/(F1F3)].sup.1/2 (4)
It will be understood by those of ordinary skill in the art that any of the
alternative configurations disclosed in U.S. Pat. No.'s 4,093,914,
5,047,726 and 5,049,828 which were disclosed with respect to the amplitude
maxima and zero phase method can also be used with the time delay maxima
process or time delay maxima and minima process depending on which of the
three cases are being used. However, instead of determining the critical
frequencies at or near the amplitude maxima and where the phase response
crosses the zero phase line, the critical frequencies are determined by
finding the frequencies at which the appropriate time delay relative
maxima occur or at which the appropriate time delay relative maxima and
minima occur depending on the particular case being used.
In the following paragraphs, three examples of the operation of the present
invention will be described. The coupled-dual resonator crystal in FIG. 4B
being operated at 11.2 megahertz ("MHz"), 21.4 MHz, and 70.2 MHz are used
as illustrative case II examples of the present invention.
FIGS. 6A through 6H graphically illustrate the measurement of the
frequencies F1, F2, F3, and F4 for calculation of FA, FB, NCF and SPSF.
Also, FIGS. 6A through 6H allow for comparison between the zero phase
process and the time delay relative maxima process in determining the
frequencies F1, F2, F3, and F4 when the coupled-dual resonator crystal is
operated at 11.2 MHz.
FIGS. 6A and 6E show the voltage amplitude responses when resonator B is
effectively short circuited (FIG. 6A) and when resonator B is effectively
open circuited (FIG. 6E) with 5 pf capacitance across it, respectively.
Similarly, FIGS. 6B and 6F show the phase responses for a short circuited
and effectively open circuited resonator B respectively. FIGS. 6C and 6G
show the time delay response with the time delay relative maxima points 72
from the phase response shown in FIGS. 6B and 6F.
Referring to FIGS. 6B and 6F for the 11.2 MHz crystal, the phase responses
have certain points 74 which cross the zero phase line 70. As described
above, the frequencies at which the phase responses cross the zero phase
line 70 will occur at or near the frequencies of the voltage amplitude
maxima. These frequencies correspond to the critical frequencies used to
calculate FA, FB, NCF and SPSF.
As shown by FIGS. 6A, 6C, 6E and 6G, the time delay maxima of the time
response occurs at the same frequency as the amplitude maxima.
Consequently, at 11.2 MHz, both the zero phase method and the time delay
maxima method can be used to measure the frequencies F1, F2, F3, and F4.
FIGS. 6D and 6H show numerical values for frequencies F1-F4 for a
coupled-dual resonator crystal operated at 11.2 MHz. Referring to FIG. 6D,
F1=11,192,747 Hz and F3=11,203,060 Hz. Referring to FIG. 6H, F2=11,196,302
Hz and F4=11,206,630 Hz. Consequently, using these values, FA=11,199,673
Hz, FB=11,196,136 Hz, SPSF=9687 Hz, and NCF=11,197,902 Hz.
Any differences between the frequencies of the amplitude maxima, the
corresponding frequencies of the zero phase crossings, and the
corresponding frequencies of the time delay maxima are on the order of
Hertz--they are slightly different because of the finite resistance of
each resonator. However, these very small differences in frequency are
negligible for purposes of determining F1, F2, F3, and F4 and calculating
FA, FB, NCF, and SPSF accurately and repeatably.
Now, referring to FIGS. 7A through 7J, the determination of the
characteristics of a 21.4 MHz crystal in FIG. 4B is described. For the
case when resonator B is short circuited, FIGS. 7A through 7C show the
amplitude response (FIG. 7A), the phase response (FIG. 7B) having several
zero phase crossings 74, and a time delay response (FIG. 7C) having maxima
points 72 and minima points 73. Referring to FIG. 7D, using the zero phase
method, F1=21388075 Hz and F3=21400875 Hz. Referring to FIG. 7E, using the
time delay relative maxima process, F1=21388287 Hz and F3=21400962 Hz.
Similarly, for the case when resonator B is effectively open circuited with
a 5 pf capacitance across it, FIGS. 7F through 7H show the amplitude
response (FIG. 7F), the phase response (FIG. 7G) having several zero phase
crossings 74, and a time delay response (FIG. 7H) having several maxima
points 72. Referring to FIG. 7I, using the zero phase method, F2=21390650
Hz and F4=21405562 Hz. Referring to FIG. 7J, using the time delay maxima
method, F2=21390750 Hz and F4=21405750 Hz.
Alternatively, it is noticed in FIG. 7E that F2 and F4 could also be
determined by the time delay minima when resonator B is short circuited
using case I.
Consequently, under the zero phase crossing method, FA=21394263 Hz,
FB=21394688 Hz, SPSF=12792 Hz, and NCF=21,394,474 Hz. Whereas, under the
time delay relative maxima method, FA=21394218 Hz, FB=21395033 Hz,
SPSF=12648 Hz, and NCF=21394624 Hz. Therefore, even though the two sets of
values for FA, FB, SPSF, and NCF are still very close to each other, the
effects of the increases in effective resonator resistances are beginning
to be measurable. Thus, even at 21.4 MHz, the improved accuracy of the
time delay relative maxima method over the zero phase method for
determining the four frequencies F1-F4 is detectable.
Next, with reference to FIGS. 8A through 8J, the process for obtaining the
four frequencies F1-F4 for a coupled-dual resonator crystal in FIG. 4B
operated at 70.2 MHz is described. When resonator B is short circuited,
FIGS. 8A through 8C show the voltage amplitude response of the crystal
(FIG. 8A), the phase response of the crystal (FIG. 8B), and the time delay
response of the crystal (FIG. 8C) with the time delay relative maxima
points 72. As shown in FIG. 8B, only one point of the phase response
touches the zero phase line 70 in the neighborhood of the amplitude
maxima.
It should be noted that the zero phase crossing method cannot be used to
determine the four frequencies F1-F4 when the phase response does not
cross the zero phase line without external compensation or using amplitude
maxima whose frequencies are already known to be functions of the
individual resonator resistances. However, the markers on FIGS. 8D and 8E
show the frequency differences when resonator B is short circuited and
FIGS. 8I and 8J show the differences in frequency when resonator B is
effectively open circuited.
Consequently, referring to FIG. 8D, F1=70,191,512 Hz and F3=70,205,562 Hz.
Referring to FIG. 8E, using the time delay relative maxima method,
F1=70,191,900 Hz and F3=70,205,912 Hz.
Similarly, when resonator B is effectively open circuited, FIGS. 8F through
8H show the amplitude response of the crystal (FIG. 8F), the phase
response of the crystal (FIG. 8G), and the time delay response (FIG. 8H)
of the crystal having several maxima points 72. As shown in FIG. 8G, the
phase response does not cross the zero phase line 70. Referring to FIG.
8I, using frequency at the amplitude maxima, F2=70,192,662 Hz and
F4=70,205,925 Hz. Referring to FIG. 8J, using the time delay relative
maxima method, F2=70,192,975 Hz and F4=70,206,200 Hz.
If we consider the frequency at which the amplitude maxima occur,
F1=70191512 Hz and F3=70205562 (see FIG. 8D) and F2=70192662 Hz and
F4=70205925 Hz (see FIG. 8I). These values, when used in equations
(1)-(4), result in the following values for FA, FB, and SPSF: FA=70202467
Hz, FB=70194608 Hz, SPSF=11646 Hz and NCF=70198537 Hz. Using the time
delay relative maxima process, F1=70191900 Hz and F3=70205912 Hz (see FIG.
8E) and F2=70192975 Hz and F4=70206200 Hz (FIG. 8J). Under the time delay
relative maxima process, using equations (1)-(4), FA=70203178 Hz,
FB=70194634 Hz, SPSF=11105 Hz and NCF=70198906 Hz.
Although the values for FB are close, the difference in values for FA and
SPSF are too large to be acceptable. Because the frequencies of the time
delay maxima tend to be independent of resistances of the resonators, the
differences between values determined by processes other than the time
delay relative maxima process will be greater in situations where the
resistances are higher and vice versa. Therefore, a coupled-dual resonator
crystal operated at 70.2 MHz cannot be measured using the a zero phase
crossing method to determine the four frequencies without an external
compensation network. If frequencies where the amplitude maxima occur are
used, errors will be produced which are a function of the size of the
effective resonator resistances and which vary from crystal to crystal.
When the frequencies at which the time delay relative maxima occur are
used, the errors are eliminated since these frequencies are independent of
the effective resonator resistances.
As shown by the three examples of coupled-dual resonator crystals at 11.2
MHz, 21.4 MHz, and 70.2 MHz, the effects of resonator resistance becomes
more pronounced as the frequency of operation of the particular
coupled-dual resonator crystal goes up. The present invention allows
measurement using the frequencies at the time delay relative maxima to
detect the four frequencies for calculating FA, FB, and SPSF very
accurately and repeatably because the frequencies of the time delay
relative maxima tend to be independent of resonator resistances.
While the preferred embodiment of the present invention has been described,
it should be appreciated that various modifications may be made by those
skilled in the art without departing from the spirit and scope of the
present invention. Accordingly, reference should be made to the claims to
determine the scope of the present invention.
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